Properties

Label 77658f
Number of curves $1$
Conductor $77658$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 77658f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77658.b1 77658f1 \([1, 1, 0, -7434, -188706]\) \(7189057/1806\) \(11416381666494\) \([]\) \(206976\) \(1.2155\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77658f1 has rank \(2\).

Complex multiplication

The elliptic curves in class 77658f do not have complex multiplication.

Modular form 77658.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 3 q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{10} + 2 q^{11} - q^{12} - 3 q^{13} + q^{14} + 3 q^{15} + q^{16} - q^{17} - q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display